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Alona [7]
3 years ago
13

Solve each equation. 9) log 4 (-a - 1) = log 4 (2a + 5)

Mathematics
1 answer:
frosja888 [35]3 years ago
5 0

 

\displaystyle\bf\\9)\\\\log_4(-a-1)=log_4(2a+5)\\\\2a+5=-a-1\\\\2a+a=-1-5\\\\3a=-6\\\\a=\frac{-6}{3}\\\\\boxed{\bf~a=-2}\\\\Verify:\\\\log_4(-a-1)=log_4(-(-2)-1)=log_4(2-1)=log_4(1)=0\\\\log_4(2a+5)=log_4(2\times(-2)+5)=log_4(-4+5)=log_4(1)=0

 

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To solve this problem, we must set up a system of equations. In this case, let's let Maggie's age be represented by the variable m and her brother's age be represented by the variable b. We are told that the sum of their ages is 24, which gives us our first equation: m + b = 24. We can construct our next equation from the first sentence of given information: b = 2m - 3. This makes our system of equations:

m + b = 24

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To solve, we are going to substitute the value for b in terms of m given by the second equation into the first equation for the variable b.

m + b = 24

m + 2m - 3 = 24

To simplify, we must first combine the variable terms on the left side of the equation using addition.

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Next, we should add 3 to both sides of the equation to get the variable term alone on the left side of the equation.

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Finally, we should divide both sides by 3 in order to get the variable m alone.

m = 9

Therefore, Maggie is 9 years old (using the first equation and substituting in this value you can find that her brother is 15 years old).

Hope this helps!

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